Start by preparing the salmon. Chop the salmon fillets into small pieces and place them in a mixing bowl.
Add the breadcrumbs, green onions, Dijon mustard, lemon juice, garlic powder, salt, and black pepper to the bowl. Mix until well combined.
Form the mixture into 4 equal patties. Place them on a plate and refrigerate for about 15 minutes to help them firm up.
While the patties chill, prepare the garlic aioli. In a small bowl, mix together the mayonnaise, minced garlic, lemon juice, and season with salt and pepper to taste. Set aside.
Heat the olive oil in a large skillet over medium heat. Once hot, add the salmon patties and cook for about 4-5 minutes on each side, or until golden brown and cooked through.
Toast the hamburger buns in the skillet for 1-2 minutes, if desired.
Assemble the burgers by placing a salmon patty on the bottom half of each bun. Top with lettuce, tomato slices, and a generous dollop of garlic aioli. Place the top half of the bun on and serve immediately.